Shell structure for concrete construction



1967 w..:. SILBERKUHL ETAL I 3,295,754

SHELL STRUCTURE FOR CONCRETE CONSTRUCTION Filed Nov. 22, 1965 4Sheets-Sheet 1 WILHELM J. SILBERKUHL UWE KASTL ERNST HAEUSSLER INVENTORSAGENT 1967 W.J. SILBERKIUHL ETAL 3,296,754

SHELL STRUCTURE FOR CONCRETE CONSTRUCTION W/LHELM J. SILBERKUHL UWEKASTL ERNST HAEUSSLER INVENTORS BY N f?" AGENT!" 1967 W.J-. SILBERKUHLETAL 3,296,754

SHELL STRUCTURE FOR CONCRETE CONSTRUCTION Filed Nov. 22, 1963 4Sheets-Sheet 5 WIL HE LM J. S/LBERKUHL U WE KASTL ERNST HAEUSSLERINVENTORS AGENT Jan. 10, 1967 W.J. SILBERKUHL ETAL 3,296,754

SHELL STRUCTURE FOR CONCRETE CONSTRUCTION Filed Nov. 22, 1963 4Sheets-$heet 4 Fig.9

Fig.

W/LHELM J. S/LBERKUHL UWE KASTL. z

ERNS T HAEUSSLER INVENTORS AGENT United States Patent 11 Claims. (c1.s2-s0 Our present invention relates to a shell structure of the generaltype disclosed in our copending application Ser. No. 168,700, filedJanuary 25, 1962, now Patent No. 3,142,136, issued July 28, 1964, i.e. aconcrete shell of substantially rectangular horizontal outline andupwardly concave transverse curvature.

Heretofore, as more particularly described in our abovementioned US.patent, such shells were preferably designed as bodies with negativeGaussian curvature conforming, at least approximately, to a one-sheethyperboloid with straight-line generatrices extending substantiallydiagonally across the rectangle, the region of these generatricesrepresenting a convenient site for the embedding of tensionedprestressing elements (e.g. steel cables) in the concrete. Otherreinforcements, e.g. in the shape of suitably curved wires or rodswithout prestress, could be embedded close to the upper and lowersurfaces of the shells.

Structures of this description, with a shell thickness of, say, 57 cm.or about 2-3", have been found satisfactory for use in various types ofroof construction as disclosed, for example, in our copendingapplication Ser. No. 133,754, filed July 21, 1961, now Patent No.3,207,054 issued September 21, 1965, in which a plurality of such shellsare disposed side by side on supporting walls or piers withinterposition of curved connecting members such as plates of corrugatedsheet material.

In these prior construction, the shells were generally of uniformthickness so that both their upper and lower surfaces had substantiallythe same approximately hyperboloidal shape. This configuration, whilesimplifying the task of the designer, imposes certain limitations uponthe load-carrying capacity of the shell structure. To increase thiscapacity, it would be necessary to deepen the concave upward curvatureof the shells, to increase their overall thickness and/or to enlargetheir width. The first of these measures is only lirnitedly feasiblebecause of manufacturing difficulties in the pouring of concrete shell-swhose sides slope upwardly at an angle greater than about 30 withreference to the horizontal. The increase in thickness is frequentlyobjectionable in that it also adds to the weight of the shell itself,thus entailing not only higher costs but also a less favorable ratio oflive to dead weight. The width of the shell, finally, is limited in thecase of precast structures by considerations of transportation andhandling.

The general object of our present invention is, therefore, to provide analternate solution for the problem of increasing the load-carryingcapacity as well as the stability of such shell structures.

A more specific object of our present invention is to provide a shell ofsuch shape that its central zone, in which the prestressing elements areconcentrated, will be strengthened without objectionable increase inoverall weight.

It is also an object of our invention to provide a shell structure ofthe general type set forth which retains its load-carrying capacity andstability even when provided with a flattened underside at its supportedends (i.e. in the region of the minor sides of the rectangle) so as tobe more conveniently deposited on building walls or other types ofpiers.

3,296,754 Patented Jan. 10, 1967 We have found, in accordance with thisinvention, that a substantial increase in the load-carrying capacity ofan upwardly concave shell can be obtained by only a partial enlargementof the shell thickness, particularly in the central transverse zone,advantageously with a gradual change in shell thickness from the middleof its central crosssection toward the ends thereof. The increased thickness enhances both the shear strength and the bending resistance of theshell but, by being confined to selected locations, does not invlove acommensurate increase in weight.

In principle, the change in thickness from the middle of the centralcross-section to its ends may be either positive or negative, thiscross-section thus assuming the shape of either a diverging or aconverging meniscus. A shell with a diverging meniscus, i.e. with agenerally bow-tieshaped central cross-section, is claimed in ourcopending application Ser. No. 325,703, filed on even date herewith. Thepresent disclosure is therefore specifically directed to shells whoseupper surface has a larger radius of transverse curvature than its lowerside, at least in the central region of the structure.

The increase in shell thickness along the central longitudinal planelowers the center of gravity of the crosssection of the shell andeffectively increases its stability. This lowering of the center ofgravity, bringing it closer to the level of the geometrical center ofthe section as compared with shell sections of uniform thickness, alsostrengthens the outwardly directed transverse :rnoments, or edgetorques, which is desirable in the presence of strong contractile forcesexerted in transverse direction, particularly in the region of thesupports, by crossed tension members within the shell.

Since the shear stresses due to the supports tend to concentrate alongthe longitudinal axis of the structure, our present improvement enhancesthe shear-resisting capacity of the shell without proportionately addingto its weight.

Another possibility afforded by our present invention is the flatteningof the underside of the shell, either throughout its length or only inthe region of the supports. According to a further feature, the uppershell surface may also be flattened in such manner that the edges of theshell progressively converge toward the median plane upon approachingthe supported sides, again with a concomitant gradual increase in themedian shell thickness.

The several modifications referred to above afford a variety of choicesfor the disposition of the generally longitudinal prestressing elements.As long as the curvature of at least the upper surface approximates thatof a one-sheet hyperboloid, the prestressing means may extendsubstantially diagonally as in the previously disclosed shells ofuniform thickness. With a flat-bottomed shell, on the other hand, thedirection of prestress may be parallel to the longitudinal edges, ifdesired. With hybrid structures, the prestressing elements may run atsome intermediate angle. These elements may be constituted by variouselongated elastic members, preferably of structural steel, e.g. in theform of one or more parallel cables or of flat ribbons.

The invention will be described in greater detail with reference to theaccompanying drawing in which:

FIG. 6 is a bottom view of the shell shown in FIGS. 1-5;

FIG. 7 is a perspective view (parts broken away), similar to FIG. 1, ofa modified shell embodying the invention;

FIG. 8 is a longitudinal sectional view taken on the line VIIIVIII ofFIG. 7;

FIGS. 9-12 are cross-sectional and end views taken, respectively, on thelines IX]X, X-X, XIXI and XII-XII of FIG. 8;

FIG. 13 is a bottom view of the shell shown in FIGS. 7-12;

FIG. 14 is a perspective view (parts broken away) of still another shellembodying the invention;

FIG. 15 is a longitudinal sectional view taken on the line XVXV of FIG.14;

FIGS. 16, 17 and 18 are cross-sectional and end views taken,respectively, on the lines XV IXVI, XVII-XVII and XVIIIXVIII of FIG. 15;and

FIG. 19 is a bottom view of the shell shown in FIGS. 14-18.

Reference will first be made to the structure of FIGS. l-6. Thisstructure comprises a concrete shell 20 of rectangular horizontaloutline and negative Gaussian curvature with an upwardly directedconcavity, the entire shell being upwardly cambered as best seen inFIGS. 2 and 3. The major sides of the rectangle are defined by a pair ofupwardly arched longitudinal edges 21, its minor sides being constitutedby edges 22 which are supported on piers 23 shown diagrammatically, indot-dash lines, in FIG. 1.

The concrete of shell 20 is reinforced by steel-Wire nettings 24 and 25,imbedded therein adjacent the lower and upper shell surfaces 27 and 28,respectively, and by prestressing elements in the form of two flat steelribbons 26 which intersect at the center C of the shell and extendnearly diagonally across the rectangle. Each tensioned ribbon 26 mayalso be replaced, as illustrated in subsequent figures, by a bank ofparallel cables numbering from one to about thirty or forty.

When seen in transverse cross-section, shell 20 has the invariable shapeof a converging meniscus, or crescent, from its center (FIG. 4) to thesupported ends 22 (FIG. Thus, each transverse section of the shell isbounded by two nearly circular arcs, approximating sections ofhyperbolas or parabolas, whose centers of curvature lie above the shell;the lower surface 28 has the smaller radius of curvature. Thelongitudinal edges 21 are of constant thickness from the center to theends 22 and are parallel to the contours of the longitudinal midsectionas seen in FIG. 2. In practice, the shell may have a minimum thicknessof about 5 to 7 cm. at the edges 21 and a maximum thickness of about tocm. at its longitudinal axis, the preferred ratio of maximum to minimumthickness ranging between approximately 1.6:1 and 2:1.

The thickening of the median longitudinal zone of the shell lowers thecenter of gravity G of its transverse section, FIGS. 4 and 5, withreference to the geometrical center C thereof so that the distance dtherebetween is considerably less than with structures of uniformthickness. The lower center of gravity G tends to give rise to outwardlydirected transverse moments or edge torques M to counteract the inwardlydirected forces created, particularly in the region of the piers 23, bythe intersecting prestressing elements 26. Toward the midpoint of theedges 21 these torques are reduced, canceled or even reversed bytransverse stresses due to the upward longitudinal camber of the shell20.

Although the prestressed ribbons 25 have been shown twisted so thattheir ends are inclined to the horizontal, it will be apparent thattheir longitudinal axes (or the central element of an equivalent arrayof Wires or cables) extend in a horizontal plane (if the slightdeviation due to their intersection is disregarded) so as to definestraight-line generatrices of an imaginary hyperboloidal 4 figure ofrevolution disposed between the upper and lower shell surfaces.

In FIGS. 7-13 we have illustrated a modified shell 30 with longitudinaledges 31 and transverse edges 32, defining a rectangular outline similarto that of shell 20 in the preceding figures. The central transversesection of the shell, seen in FIG. 9, is again substantially in theshape of a converging meniscus with generally hyperbolical curvaturewhile being slightly flattened at the center of its convex side, owingto the presence of a flat bottom surface 37 which widens from the centertoward the minor sides 32 so as to extend over the full width of theshell at the supported ends thereof. These ends, therefore, can rest onlevel-topped piers 33 (FIG. 7) representative of walls, beams, girdersand the like, in contrast to the specially shaped piers 23 of shell 20(FIG. 1). In the median longitudinal plane, as shown in FIG. 8, thelower and upper shell surfaces 37, 38 are both substantially horizontalso that the thickness of the shell remains constant along the median.The maximum thickness at the midpoint of the central shell section, seenin FIG. 9, again exceeds the minimum thickness at the edges 31 by afactor ranging between, preferably, about 1.6 and 2.

As will be apparent from FIG. 7, the transverse section of shell 30changes from a crescent shape at the center to a lano-convex shape atthe supported ends 32 so that the curvature of its upper surface 38 isinverted in the vicinity of these ends. The region of inversion, inwhich the surface 38 flattens out, is seen in FIG. 11. The wire nettingsextending close to these surfaces and conforming thereto have beenomitted in FIGS. 8-12 but the lower netting is visible at 34 in FIG. 7.Shell 30 also has prestressing means, disposed between these nettings,in the form of an array of rods or wires 36 of structural steel passingunder tension along the longitudinal axis of the shell, this in adirection parallel to its edges 31; it will be apparent that the shellwould also accommodate horizontal wires or the like disposed at a smallangle to this axial direction. Naturally, the members 36 could also bereplaced by one or more flat ribbons as in the first embodirnent.

In FIGS. l4l9 we show a shell 40 whose longitudinally concave underside47 flattens out toward the supported ends 42 (the supporting piershaving been omitted in these figures) and which, in addition tounstressed steel- Wire nettings (of which the lower one is visible at 44in FIG. 14), incorporates prestressing means in the form of two sets ofcables 46 that are inclined to the longitudinal axis at somewhat smallerangles than the ribbons 26 of FIGS. 16. The median shell thickness isagain approximately constant, increasing but slightly from the center tothe supported edges 42 in the plane seen in FIG. 15. In thislongitudinal plane the top surface 48 is convex and substantiallyparallel to the concave lower surface 47; its transverse concavity, asshown in FIGS. 16-18, becomes progressively shallower and narrowertoward the minor sides 42 or the rectangular outline, owing to aflattening of the edges 41 which thus broaden horizontally as theyapproach these sides. The result, as seen in the end view of FIG. 18, isa considerable increase in cross-sectional area at the ends, withcorresponding strengthening of the shell in the region where thetensioned cables 46 (or equivalent ribbons) are anchored and thestresses due to the load are transferred to the supports. The centralcross-section of shell 40 (FIG. 16) is similar to those of shells 20 and30.

If the central transverse cross-sections of shell 20, 30 or 40 (FIGS. 4,9 and 16) were given the shape of a diverging rather than convergingmeniscus, i.e. if the radius of curvature of the upper shell surfacewere made smaller than that of the lower surface in that plane, thecenter of gravity of this central shell section would rise. This wouldtend to intensify the inwardly directed edge torques and, while reducingthe stability of the shell, would further increase its load-carryingcapacity. An-

other effect would be a shifting of the moment line of that sectiontoward the compression flange thereof, i.e. toward the upper shellsurface. This is advantageous in many instances in which it has beenobserved that, in the case of prior structures, the upper flange reachesits permissible limit of compression while the stresses within the lowerflange are still well below the maximum tension allowed under thebuilding code. Because of this rather unexpected phenomenon, shells ofconstant thickness do not always have a loading capacity commensuratewith the tensile strength of the material, yet with shells of outwardlyflared central cross-section this drawback is obviated through aredistribution of stresses so that both the compressive and the tensilestrength of the concrete are fully utilized. This has been described inour aforementioned copending application Ser. No. 325,703, where suchshells have been specifically claimed.

What is claimed is:

1. A structure adapted to be used in roof construction and the like,comprising a concrete shell of substantially rectangular horizontaloutline with upwardly arched longitudinally edges at the longer sides ofthe rectangle, said shell being of upwardly concave transverse curvatureat least over the major part of its surface and having a substantiallycrescent-shaped central cross-section, and .reinforcing means imbeddedwithin the body of said shell, said shell having a low center of gravityand being substantially free from edge torques in the region of saidcentral cross-section.

2. A structure as defined in claim 1 wherein said shell is ofsubstantially uniform transverse cross-section throughout its length.

3. A structure as defined in claim 2 wherein said shell is upwardlycambered in longitudinal direction.

4. A structure as defined in claim 1 wherein said shell has a fiatunderside at least in the region of the minor sides of the rectangle.

5. A structure as defined in claim 4 wherein said shell has fiat uppersurfaces extending inwardly from its longitudinal edges in the region ofsaid minor sides.

6. A structure as defined in claim 4 wherein said flat underside extendssubstantially horizontally over the full length of the shell and widensfrom the center to said minor sides.

7. A structure as defined in claim 6 wherein said reinforcing meansincludes an elongated elastic member extending under tensionsubstantially along the longitudinal median plane of the shell.

8. A structure as defined in claim 1 wherein saidreinforcing meansincludes steel-wire nettings extending close 6 t0 the upper and lowershell surfaces over the full length and width of the shell.

9. A structure as defined in claim 8 wherein said reinforcing meansfurther includes at least one steel ribbon extending under tension ingenerally longitudinal direction between said nettings from one of theminor sides of the rectangle to the other.

10. A structure adapted to be used in roof construction and the like,comprising a concrete shell of substantially rectangular horizontaloutline with upwardly arched longitudinal edges at the longer sides ofthe rectangle, said shell being of upwardly concave transverse curvatureat least over the major part of its surface and having a substantiallycrescent-shaped central cross-section, and elongated prestressing meansextending under tension in generally longitudinal direction from one ofthe minor sides of the rectangle to the other minor side Within the bodyof said shell, said shell having a low center of gravity and beingsubstantially free from edge torques in the region of said centralcross-section.

11. A structure adapted to be used in roof construction and the like,comprising a concrete shell of substantially rectangular horizontaloutline with upwardly arched longitudinal edges at the longer sides ofthe rectangle, said shell being of upwardly concave transverse curvatureat least over the major part of its surface and having a substantiallycrescent-shaped central cross-section, and elongated prestressing meansextending under tension in generally longitudinal direction from one ofthe minor sides of the rectangle to the other minor side within the bodyof said shell, the thickness of the shell Varying between the middle andthe ends of said central cross-section by a factor of substantially 1.6to 2, said shell having a low center of gravity and being substantiallyfree from edge torques in the region of said central cross-section.

References Cited by the Examiner UNITED STATES PATENTS 9/1906 Luten52-88 FOREIGN PATENTS 838,294 12/1938 France.

1. A STRUCTURE ADAPTED TO BE USED IN ROOF CONSTRUCTION AND THE LIKE,COMPRISING A CONCRETE SHELL OF SUBSTANTIALLY RECTANGULAR HORIZONTALOUTLINE WITH UPWARDLY ARCHED LONGITUDINALLY EDGES AT THE LONGER SIDES OFTHE RECTANGLE, SAID SHELL BEING OF UPWARDLY CONCAVE TRANSVERSE CURVATUREAT LEAST OVER THE MAJOR PART OF ITS SURFACE AND HAVING A SUBSTANTIALLYCRESCENT-SHAPED CENTRAL CROSS-SECTION, AND REINFORCING MEANS IMBEDDEDWITHIN THE BODY OF SAID SHELL, SAID SHELL HAVING A LOW CENTER OF GRAVITYAND BEING SUBSTANTIALLY FREE FROM EDGE TORQUES IN THE REGION OF SAIDCENTRAL CROSS-SECTION.